I think C1 is going to be filtering out some of the, already very small, AC signal.
Looks like the AD737 chip (http://www.analog.com/en/special-linear-functions/rms-to-dc-converters/ad737/products/product.html) might be the device for you. It converts an AC signal up to 200 mV to a DC signal.
This Application Note gives some suggested circuits:
http://www.analog.com/static/imported-files/application_notes/AN-268.pdf